A232955 -id:A232955 - cp's OEIS frontend

A232949 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

1, 21, 1881, 685251, 1074244299, 7168373617095, 205030957086979647, 25121788915317351455997, 13201474923932116066095060171, 29758989052767328125373420316820645

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

Diagonal of A232955

			Some solutions for n=3
..0..2..0....0..1..0....0..1..0....0..1..0....0..2..0....0..0..1....0..1..3
..3..2..3....3..2..3....1..0..0....1..0..1....3..2..3....0..0..1....1..1..1
..2..3..2....3..1..0....0..0..2....2..3..1....3..2..0....0..1..0....0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..11

A232950 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

9, 129, 1881, 27441, 400329, 5840289, 85202361, 1242993681, 18133691049, 264547403649, 3859408908441, 56303849204721, 821401284620169, 11983196174074209, 174819534903392121, 2550393846506436561

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

			Some solutions for n=4:
..0..1..3....0..1..0....0..0..0....0..1..3....0..2..0....0..0..0....0..0..0
..0..2..3....3..2..0....0..1..0....1..1..3....0..1..3....2..2..2....2..0..0
..2..2..2....0..2..2....0..0..0....0..1..1....1..1..0....2..3..2....2..0..2
..0..2..3....3..2..3....2..0..0....0..1..1....3..1..3....3..3..2....0..0..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 3 of A232955.

Empirical: a(n) = 15*a(n-1) - 6*a(n-2).
Conjectures from Colin Barker, Oct 06 2018: (Start)
G.f.: 3*x*(3 - 2*x) / (1 - 15*x + 6*x^2).
a(n) = (2^(-1-n)*((15-sqrt(201))^n*(-3+sqrt(201)) + (3+sqrt(201))*(15+sqrt(201))^n)) / sqrt(201).
(End)

A232951 Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

27, 771, 22971, 685251, 20442651, 609853251, 18193384251, 542752261251, 16191600916251, 483034266181251, 14410069980856251, 429886928094781251, 12824557492939156251, 382587290147700781251, 11413495916966327656251

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

			Some solutions for n=3:
..0..0..0..1....0..2..3..1....0..2..3..2....0..0..1..1....0..2..2..2
..0..0..0..2....0..1..0..2....0..2..3..2....2..0..1..3....3..2..2..2
..0..0..0..1....0..2..3..2....0..2..3..1....1..3..2..0....0..2..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 4 of A232955.

Empirical: a(n) = 31*a(n-1) - 35*a(n-2) + 5*a(n-3).
Conjectures from Colin Barker, Oct 06 2018: (Start)
G.f.: 3*x*(9 - 22*x + 5*x^2) / ((1 - x)*(1 - 30*x + 5*x^2)).
a(n) = (55 + (15-2*sqrt(55))^n*(55+sqrt(55)) - (-55+sqrt(55))*(15+2*sqrt(55))^n)/55.
(End)

A232952 Number of nX5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

81, 4629, 283131, 17429409, 1074244299, 66226131273, 4082986991091, 251727862281441, 15519780149309307, 956841601733733945, 58992197961597648195, 3637048689898637056977, 224235130894279830031179

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

Column 5 of A232955

			Some solutions for n=2
..0..0..2..2..0....0..1..3..1..3....0..2..0..2..0....0..0..0..0..2
..1..0..2..2..0....0..1..3..3..1....0..1..3..2..2....2..0..1..0..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 78*a(n-1) -1043*a(n-2) +2012*a(n-3) +10236*a(n-4) -39726*a(n-5) +41724*a(n-6) -6408*a(n-7) -8680*a(n-8) +2592*a(n-9) -96*a(n-10)

A232953 Number of nX6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

243, 27771, 3484893, 442227825, 56282275743, 7168373617095, 913176469752921, 116335186551225981, 14820857088037937067, 1888152565941258630963, 240547722416361692415285, 30645415985954670300604329

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

Column 6 of A232955

			Some solutions for n=2
..0..0..1..3..2..2....0..0..2..3..3..3....0..1..0..0..0..0....0..1..1..1..3..1
..1..1..1..3..2..0....0..0..2..3..1..3....0..2..0..0..1..0....1..0..0..1..1..3

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 164*a(n-1) -4626*a(n-2) -10237*a(n-3) +724806*a(n-4) -2489128*a(n-5) -20967827*a(n-6) +129949639*a(n-7) -92364571*a(n-8) -632285585*a(n-9) +1013530592*a(n-10) +686481298*a(n-11) -1825492832*a(n-12) +98427893*a(n-13) +965164167*a(n-14) -223865096*a(n-15) -150502642*a(n-16) +39404908*a(n-17) +4977174*a(n-18) -881024*a(n-19) -36192*a(n-20) +4272*a(n-21)

A232954 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

729, 166629, 42904365, 11228712351, 2953363127697, 777971521023633, 205030957086979647, 54043267342289534097, 14245737532796759368533, 3755217033315506600279775, 989890841378547325619047929

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

Column 7 of A232955

			Some solutions for n=2
..0..2..0..2..3..2..2....0..2..0..1..1..3..3....0..0..1..3..2..3..2
..2..0..0..1..0..2..3....3..2..0..0..1..3..1....0..1..1..3..2..2..2

R. H. Hardin, Table of n, a(n) for n = 1..210

A232956 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

4, 21, 129, 771, 4629, 27771, 166629, 999771, 5998629, 35991771, 215950629, 1295703771, 7774222629, 46645335771, 279872014629, 1679232087771, 10075392526629, 60452355159771, 362714130958629, 2176284785751771

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

			Some solutions for n=5:
..0..1..0..2..3....0..0..0..0..1....0..0..0..1..0....0..1..1..1..0
..3..2..0..2..2....0..1..1..0..2....0..0..1..1..0....0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 2 of A232955.

Empirical: a(n) = 5*a(n-1) + 6*a(n-2).
Conjectures from Colin Barker, Oct 06 2018: (Start)
G.f.: x*(4 + x) / ((1 + x)*(1 - 6*x)).
a(n) = (25*6^n - 18) / 42 for n even.
a(n) = (25*6^n + 18) / 42 for n odd.
(End)

A232957 Number of 3 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

16, 147, 1881, 22971, 283131, 3484893, 42904365, 528197043, 6502696923, 80055386493, 985570487037, 12133464037491, 149376378762507, 1838988638568957, 22639986598509837, 278723306070050355

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

			Some solutions for n=4:
..0..0..1..1....0..0..0..0....0..1..0..0....0..1..1..1....0..1..1..1
..0..1..1..0....1..1..1..1....0..1..1..0....3..1..1..3....0..0..0..1
..0..0..0..1....1..0..1..0....0..0..1..1....3..1..3..1....1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 3 of A232955.

Empirical: a(n) = 12*a(n-1) + 7*a(n-2) - 40*a(n-3) + 12*a(n-4).

Empirical g.f.: x*(16 - 45*x + 5*x^2 + 10*x^3) / (1 - 12*x - 7*x^2 + 40*x^3 - 12*x^4). - Colin Barker, Oct 06 2018

A232958 Number of 4Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

64, 1029, 27441, 685251, 17429409, 442227825, 11228712351, 285082486341, 7238105184837, 183771148650939, 4665845904118053, 118463173683294573, 3007712801760687567, 76364121654785540601, 1938841730920089921489

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

Row 4 of A232955

			Some solutions for n=3
..0..1..0....0..1..0....0..2..0....0..0..0....0..1..3....0..2..0....0..1..1
..0..1..3....3..2..0....2..0..2....2..2..0....3..1..0....3..2..0....1..1..3
..0..2..3....0..2..2....2..2..2....3..2..3....0..2..3....3..2..0....3..1..0
..3..2..0....0..2..3....2..3..3....0..1..0....3..1..3....3..1..0....3..2..3

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 24*a(n-1) +76*a(n-2) -1008*a(n-3) -992*a(n-4) +8762*a(n-5) -7403*a(n-6) -2174*a(n-7) +3324*a(n-8) -416*a(n-9) -96*a(n-10)

A232959 Number of 5Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

Original entry on oeis.org

256, 7203, 400329, 20442651, 1074244299, 56282275743, 2953363127697, 154964050219677, 8131839344628711, 426724728385684671, 22392882542866505109, 1175093728648087275513, 61664507065517646615231

Offset: 1

R. H. Hardin, Dec 02 2013

nonn

Row 5 of A232955

			Some solutions for n=2
..0..0....0..1....0..2....0..1....0..1....0..1....0..0....0..0....0..1....0..0
..1..0....0..0....3..2....3..1....1..0....0..2....0..2....1..1....3..2....2..2
..2..3....2..2....0..1....3..3....2..0....3..2....2..0....0..0....2..3....2..2
..2..0....2..2....0..1....1..3....1..3....2..2....2..2....0..0....1..0....2..2
..2..2....2..2....3..2....3..1....1..3....2..2....3..3....2..0....0..0....2..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 67*a(n-1) -533*a(n-2) -15660*a(n-3) +183231*a(n-4) +657345*a(n-5) -14397321*a(n-6) +26479475*a(n-7) +308726752*a(n-8) -1394230594*a(n-9) -93496336*a(n-10) +10567010405*a(n-11) -15260787758*a(n-12) -20784722042*a(n-13) +61450333950*a(n-14) -11848262788*a(n-15) -72270718040*a(n-16) +48716606000*a(n-17) +23916567320*a(n-18) -26795989184*a(n-19) -10634656*a(n-20) +4071926912*a(n-21) -391701632*a(n-22) -188446976*a(n-23) +19444224*a(n-24) +1963008*a(n-25) -110592*a(n-26) for n>27

cp's OEIS Frontend

A232949 Number of n X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232950 Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232951 Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232952 Number of nX5 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232953 Number of nX6 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232954 Number of nX7 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232956 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232957 Number of 3 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232958 Number of 4Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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A232959 Number of 5Xn 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.

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